非同步机电源接入电网后的谐振问题分析及抑制

随着非同步机电源在电网中的占比越来越大，有别于传统功角振荡的电网谐振不稳定问题逐渐显现。为此，文中提出了一种基于s域节点导纳矩阵的网络谐振分析方法，用以分析及抑制含非同步机电源电力系统的谐振问题。首先，介绍了两种非同步机电源的s域阻抗建模方法——小干扰线性化法和测试信号法，重点考虑了内环控制器和锁相环的影响。然后，给出了一套基于s域节点导纳矩阵的网络谐振结构分析方法，并提出了两个描述谐振模式的特征指标，用以确定其主要影响区域和敏感元件参数。最后，以某风电场并网系统为例，对该系统的谐振结构进行了分析，并针对其存在的谐振问题提出了相应的改善措施。分析表明，由于电力电子装置的负电阻效应，含非同步机电源的电力系统确实存在谐振不稳定的风险，需要加以抑制。     

Short-circuit admittance matrix synthesis with rc common-ground networks and a minimum number of grounded finite-gain phase-inverting voltage-controlled voltage sources

A new procedure for the synthesis of active RC networks when grounded finite-gain phase-inverting voltage-controlled voltage sources serve as active elements is developed. It is proved that an arbitrary n × n matrix of real rational functions of the complex frequency variable can be realized as the short-circuit admittance matrix of a grounded transformerless active RC n-port network containing (n+1) grounded finite-gain phase-inverting voltage-controlled voltage sources (VCVSs). In general all the (n+1) grounded VCVSs are necessary. The structure proposed to prove a general theorem is later simplified for the realization of a restricted but important class of real rational matrices to obtain considerable savings in the computation volume and in the number of passive components used for the realization of the network. Examples are given to illustrate presented synthesis procedures.     

Identification of the return difference matrix of a multivariable linear control system,in terms of its inverse closed-loop transfer matrix

The return difference matrix F (s) of a multivariable control system with respect to its gain elements is obtainable directly from the inverse transfer matrix T ^?1(s), which is in turn derived (by elimination of undriven node groups) from the coefficient matrix of the set of independent differential equations describing the system. Thus, no knowledge of the system's topology is required in order to obtain F (s). Furthermore, the inverse of one of the submatrices of T ^?1(s) yields the idealized response, if all gain elements are assumed to exhibit infinite gain.     

Developments in the Newton Raphson power flow formulation based oncurrent injections

This paper describes a sparse Newton Raphson formulation for the solution of the power flow problem, comprising 2n current injection equations written in rectangular coordinates. The Jacobian matrix has the same structure as the (2n×2n) nodal admittance matrix, in which each network branch is represented by a (2×2) block. Except for PV buses, the off-diagonal (2×2) blocks of the proposed Jacobian equations are equal to those of the nodal admittance matrix. The results presented show that the proposed method leads to a substantially faster power flow solution, when compared to the conventional Newton Raphson formulation, expressed in terms of power mismatches and written in polar coordinates     

电力网络的谐振稳定性分析方法研究

随着电力系统电力电子化程度的不断加深,近年来出现了多起机理不明的新的振荡现象。提出了电力网络谐振稳定性的概念,试图将上述机理不明的振荡现象纳入到电力网络的谐振不稳定范畴,从而基于线性网络理论对众多复杂振荡现象进行分析,为借助数学上完全成熟的线性系统理论解决电力系统实际问题提供一条途径。围绕判断谐振稳定性的分析方法展开,通过引入电力网络的s域节点导纳矩阵,将电力网络的谐振稳定性问题归结为判断s域节点导纳矩阵行列式的零点在复平面上的分布问题。首先,理论证明了s域节点导纳矩阵行列式的零点就是系统的特征值。其次,给出了求解s域节点导纳矩阵行列式零点的实部-虚部交叉迭代法。接着,推导了特定谐振模式下的节点电压振型和参与因子矩阵,这2个指标可用来定位特定谐振模式发生的位置。最后,通过算例展示了所提方法在分析电力网络谐振稳定性方面的有效性。     

Switched capacitor filters with a row dominant nodal admittance matrix

Stray capacitance insensitive switched capacitor filters are studied, whose nodal admittance matrix is row-dominant for arbitrary capacitor values. Such filters have low passband sensitivities, because their transfer function is intrinsically bounded by 1, as is the case for LC-filters. Furthermore, row-dominant filters have the additional advantage that internal voltages are bounded by one, and reach this bound at each attenuation zero, which ensures optimal dynamic range. However, we show that the attenuation zeros of row-dominant filters are located at the frequencies z² with (z²)^m = 1, where m is smaller than or equal to the number of operational amplifiers. Therefore, such filters are not suitable for conventional filter applications. Two examples of such filters are given.     

Synthesis of n-port active rc networks with a minimum number of capacitors

A new and practical synthesis procedure is presented for the realization of an arbitrary n × n matrix of real rational functions of the complex frequency variable as the short-circuit admittance matrix of a transformerless active RC n-port network. The realization requires a theoretically minimum number of capacitors p, where p is the degree of the matrix, and no more than (n + p + 1) grounded finite-gain phase-inverting voltage-controlled voltage sources. All the capacitors and ports are grounded. The freedom implicit in the synthesis procedure allows the inclusion of constraints on the passive element values. Furthermore, in special cases the realization is achieved with a reduced number of conductances and voltage-controlled voltage sources. The synthesis procedure is simple to apply and can readily be implemented on a digital computer. Several examples are given.     

Three-phase power flow calculations using the current injectionmethod

This paper presents a new sparse formulation for the solution of unbalanced three-phase power systems using the Newton-Raphson method. The three-phase current injection equations are written in rectangular coordinates resulting in an order 6n system of equations. The Jacobian matrix is composed of 6×6 block matrices and retains the same structure as the nodal admittance matrix. Practical distribution systems were used to test the method and to compare its robustness with that of the backward/forward sweep method     

Approximate formulae for numerical inversion of Laplace transforms

Most methods for the numerical calculation of inverse Laplace transformations f(t) = L⁻¹[F(s)] have serious limitations concerning the class of functions F(s) that can be inverted or the achievable accuracy. The procedures described in the paper can be used to invert rational as well as irrational or transcendental functions of the complex variable s. The required accuracy of the results can be enhanced without changing the algorithm, only at the cost of a longer computation time. The described methods were verified with many examples including transients in lumped/distributed systems with sections of lossy multiconductor transmission lines or with distributed RC elements. © 1998 John Wiley & Sons, Ltd.     

基于高斯方法及Sherman-Morrison公式的暂态稳定性并行计算方法

并行计算是实现大规模电力系统暂态稳定性实时分析计算的有效途径。将s级2s阶的高斯方法和扩展的Sherman-Morrison矩阵求逆公式相结合,提出了一类新的暂态稳定性并行计算方法。该方法首先利用s级2s阶的高斯方法对微分-代数方程组进行多级离散,并利用严格的牛顿法对离散后的非线性方程组进行整体求解。在此基础上,按s个时间点将整体雅可比矩阵分裂成为一个分块对角矩阵和一个分块常系数矩阵。然后,以分裂后的分块对角矩阵为基础,利用扩展的Sherman-Morrison矩阵求逆公式将s个时间点上的计算任务进行“解耦”。所提方法在保持严格牛顿法的收敛性的同时具有很好的并行性。利用OpenMP并行计算技术在多核计算机上对2个不同的系统算例进行了测试,结果表明,所提出的并行方法可以获得较好的加速比以及并行效率。     

On rlc network matrices

A generalization of the coefficient conditions which hold for an RLC network as well as of the paramount property obeyed by the matrix of a resistance network is derived. This result is a property of either the nodal or mesh matrices for either the admittances or impedances of a general RLC network. It states that if P is any principal minor or such a matrix and Q any other minor constructed from the same rows (columns) as P then P, P + Q, P–Q are rational functions of the complex frequency variable which, before cancellation of common factors, have only non-negative coefficients.     

FAST ACCURATE TRANSIENT STABILITY SIMULATIONS

ABSTRACT

The paper describes a Simultaneous Implicit (SI) approach for transient stability simulations based on an iterative technique using traingularised admittance matrix [1]. The reduced saliency of generator in the subtransient state is taken advantage of to speed up the algorithm. Accordingly, generator differential equations, except rotor swing, contain voltage proportional to fluxes in the main field, dampers and a hypothetical winding representing deep flowing eddy currents, as state variables. The simulation results are validated by comparison with two independent methods viz. Runge-Kutta simulation for a simplified system and a method based on modelling damper windings using conventional induction motor theory[2].     

Steady-state load shedding schemes: a performance comparison

This paper presents a formulation of the optimal steady-state load shedding problem that uses the sum of the squares of the difference between the connected active and reactive load and the supplied active and reactive power. The latter are treated as dependent variables modelled as functions of bus voltages only. The equality constraints associated with the power system load curtailment problem are the power flow equations in polar form utilizing the nodal admittance matrix approach. The inequality constraints are characterized by limits on line flows, voltage magnitudes and angles, and active and reactive power generations. The MINOS nonlinear optimization package is used to implement the optimization process. Testing is done using IEEE 14- and 30-bus power systems, and results obtained. The optimal results are compared with results obtained using two earlier approaches. The results obtained using the proposed approach appear to give a better optimal state of the power system.     

Synthesis of n‐port resistive networks containing 2n terminals

This paper is concerned with the realizability problem of n‐port resistive networks that contain 2n terminals. A necessary and sufficient condition for any real symmetric matrix to be realizable as the admittance of an n‐port resistive network containing 2n terminals is obtained. This condition is based on the existence of a parameter matrix. Furthermore, the values of the elements are expressed in terms of the entries of the admittance matrix and the parameter matrix. Finally, a numerical example is used to illustrate the results. Copyright © 2013 John Wiley & Sons, Ltd.     

A class of nonrealizable paramount matrices

Although paramountcy¹ is a necessary and sufficient condition for the realizability of a 3 by 3 matrix as either an open-circuit impedance matrix or a short-circuit admittance matrix of a resistive 3-port,² Weinberg's 4 by 4 example^3,5 shows that paramountcy, although necessary for open-circuit impedance realization, is not sufficient. Here we exhibit a class of 4 by 4 completely irreducible paramount matrices, including Weinberg's example, no member of which is realizable as an open-circuit impedance matrix. This is accomplished by examining those topological constraints inherited by a realizing network when algebraic conditions are imposed on the paramount matrix which the network realizes. Our development deals with an n-port network, for arbitrary n, and also provides new criteria guaranteeing nonrealizability of an irreducible¹ paramount matrix.     

Parallel Simulation of Power Systems Transient Stability Based on Implicit Runge–Kutta Methods and W-transformation

This paper presents a novel parallel algorithm for power systems transient stability simulation based on fully implicit Runge–Kutta (IRK) method. The s-stage IRK method is used to convert the differential-algebraic system simultaneously at s different time points into a set of non-linear algebraic equations, and the algebraic system is then solved by Newton's method. By the use of the matrix factorization technique, the solution of the linear equations involved in Newton's process is divided into two parts: the first part is decoupled at s different time points, thus it is fully parallelizable in time, and the second part is solved by preconditioned generalized minimal residual method (GMRES) method, while a new preconditioning method has been proposed by using the W-transformation and double-parameters method. For test, the proposed algorithm is implemented on multiple-graphics processing units (GPUs) computing platform. The results show that the proposed algorithm is accurate and has good convergence. Moreover, the parallel algorithm implemented on multiple-GPUs computing platform achieves high parallel efficiency.     

Dynamische Netzberechnung mit dem Zeitkonstantenverfahren

Übersicht Bei der Berechnung elektrischer Versorgungsnetze sind die Netzgleichungen in eine simulationsfähige Form zu überführen. Dies läßt sich durch die Zustandsvariablenmethode oder das Differenzenleitwertverfahren erreichen. Ebenso geeignet ist das Zeitkonstantenverfahren, das in dieser Arbeit vorgestellt und mit den beiden anderen Methoden verglichen wird. Das Zeitkonstantenverfahren formt die Netzgleichungen im zeitkontinuierlichen Bereich um. Der Netzaufbau läßt sich durch ein Strukturbild beschreiben und verändert sich nicht bei Schalthandlungen.

---

Simulation of power system dynamics using the time constant method

Contents The state variable method or the nodal admittance matrix method are usually used in power system dynamics simulation. In this paper a new algorithm, the time constant method, is proposed and compared with the two other algorithms. The time constant method transforms the network equations in the time continuous domain. The structure of the power system can be modelled by a block diagram and does not change during switching operations.

     

General approaches to efficient d-q simulation and model translation for synchronous machines: a recap

This paper summarizes some recent findings in the area of synchronous machine modeling by means of equivalent circuits of arbitrary order. This allows us to propose a concise analytical expression to be derived for the admittance matrix and yields a structure of the state matrices which facilitates their numerical evaluation. By organizing the parameters into two structured vectors, we show how to calculate the state matrices and admittance matrix of generalized models of machine by means of MATLAB programs. The techniques are proposed for passing from the equivalent circuits to the operational impedances and vice-versa. Lastly, we transpose the conventional electromechanical state equations into our generalized modeling framework and derive new formulas for the matrices used in the eigenvalue analysis of synchronous motors and generators. Besides conventional stability studies, the present approaches along with the MATLAB toolbox could be useful for machine-converter system optimization, motor starting problems, digital TNA implementation and machine models identification. The latter application is investigated in particular with a view to enhancing current methods used to analyse short-circuit oscillograms recorded during the commissioning of large utility grade generators and synchronous condensers.     

New transformation polynomials for discretization of analogue systems

The novel transformation polynomials for discretization of analogue systems have been presented. A generalization of some of the existing transformation methods has also been done. A comparative analysis, through the corresponding examples involving several known discretization methods, has been carried out. It has been demonstrated that the application of these transformation polynomials allows the reduction of discretization error compared to other approximation methods. The response to an arbitrary excitation of the discrete system obtained by these transformations is approximately equal to that of the original analogue system. The transformations are rational since variable s ^{− n} ,n ∈ N, transforms to the quotient of two linear functions of variable z.